In a process control, major role of a controller is to suppres the effects of disturbances and to keep the controlled value constant. To have a good control condition, parameters of a controller should be adjusted to optimum condition. This optimum adjustment is an interesting problem, it is however more important to know how well the process is controlled by the optimaly adjusted controller. In this article, the author intends to have a quantitative representation of quality of control. Disturbances are assumed to belong to a stationary random process and to be characterised by a deviation σ
d2 and a half-power frequency ω
0. To express controllability of a controller, the ratio of the deviation of the controlled value to the deviation of disturbance is defined as the statistical control coefficient. The minimum value of this statistical control coefficient in all adjustable parameters for the given random disturbance expresses the limit of control which can be realized by the controller. Minimum values of statistical control coefficient for P, PI, PD and PID controllers were numerically calculated. From this result, the controllability of various types of controllers were compared and PID controller was proved to give the best quality of control against random disturbances. If an allowable limit of a statistical control coefficient is presumably given, a practical limit of ω
0 is found for the given process.
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